In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by bilevel PROGRAMMING (BLP) problems, where in each level one must optimize some OBJECTIVE functions. There are so many algorithms in order to find the global optimum of the LINEAR version of BLP problems. This paper addresses multi-OBJECTIVE LINEAR bilevel multi-follower PROGRAMMING (MOLBMFP) problems in which there is no sharing information among followers. It presents a new method for solving these problems.

In this paper, we establish a proof for a necessary condition for MULTIPLE OBJECTIVE fractional pro-gramming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.

In this article, multi-OBJECTIVE LINEAR PROGRAMMING problems with interval coefficients in OBJECTIVE functions are investigated. By using the acceptance index, the concepts of different answers corresponding to such problems are presented. In order to achieve such answers, a new solution method is introduced. Characteristics of the answer/answersobtained from the new solution method are also expressed. For example, the unique optimal solution resulting from thenew solution method is a strict A-efficient solution of the multi-OBJECTIVE LINEAR PROGRAMMING problem with interval coefficients in the OBJECTIVE functions. In order to better understand the presented concepts and solution method, numerical examples are also examined.

MULTIPLE OBJECTIVE PROGRAMMING (MOP) problems have become famous among many researchers due to more practical and realistic implementations. There have been a lot of methods proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP problems by starting from a utopian point (which is usually infeasible) and moving towards the feasible region via stepwise movements and a plain continuous interaction with Decision Maker (DM). We consider the case where all OBJECTIVE functions and constraints are LINEAR. The implementation of the proposed algorithm is demonstrated with two numerical examples.